Depends on the team. Not every team has a player capable of doing it, and has enough other quality players to make up for it. Hazard didn't handle it well, but worse of all the rest of the team didn't make up for it.
Yea, Herrera played an excellent game. One of the best of his United career.
That's basically an impossible standard to play to on a regular basis, especially for lower quality teams, so shutting down Hazard like that isn't something I'd expect teams to be able to pull off with any form of regularity. Plus if it goes a little wrong, you get the FA cup fixture where Herrera picked up an early yellow and then United had to have others help out, who ran up the fouls which led to Herreras second yellow.
And as you mentioned, the rest of United played excellent. How many times did you see a Chelsea pass that looked dangerous when it left the foot only to be casually intercepted. If United play like they did yesterday, they can play with any team in Europe. But that's a big if and they've only done it a couple times all year.